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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2020, Volume 61, Issue 2, Pages 40–59
DOI: https://doi.org/10.15372/PMTF20200205 (Mi pmtf338) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Group analysis of one-dimensional gas dynamics equations in Lagrangian coordinates and conservation laws

Ch. Kaewmaneea, S. V. Meleshkob

a Naresuan University, 65000, Phitsanulok, Thailand
b School of Mathematics, Institute of Science, Suranaree University of Technology, 30000, Nakhon Ratchasima, Thailand
Full-text PDF (1077 kB) Citations (1)
DOI: https://doi.org/10.15372/PMTF20200205
Abstract: A group analysis of the second-order equation including one-dimensional gas dynamics equations in Lagrangian coordinates as a particular case is performed. The use of Lagrangian coordinates makes it possible to consider one-dimensional gas dynamics equations as a variational Euler–Lagrange equation with an appropriate Lagrangian. Conservation laws are derived with the use of the variational presentation and Noether theory. A complete group classification of the Euler–Lagrange equation is obtained; as a result, 18 different classes can be classified.
Keywords: group analysis, gas dynamics equations, Lagrangian coordinates, group classification, conservation laws.
Funding agency Grant number
Naresuan University
Russian Science Foundation 18-11-00238
Received: 14.10.2019
Revised: 14.10.2019
Accepted: 28.10.2019
English version:
Journal of Applied Mechanics and Technical Physics, 2020, Volume 61, Issue 2, Pages 189–206
DOI: https://doi.org/10.1134/S0021894420020054
Bibliographic databases:
Document Type: Article
UDC: 517.9
Language: Russian
Citation: Ch. Kaewmanee, S. V. Meleshko, “Group analysis of one-dimensional gas dynamics equations in Lagrangian coordinates and conservation laws”, Prikl. Mekh. Tekh. Fiz., 61:2 (2020), 40–59; J. Appl. Mech. Tech. Phys., 61:2 (2020), 189–206
Citation in format AMSBIB
\Bibitem{KaeMel20}
\by Ch.~Kaewmanee, S.~V.~Meleshko
\paper Group analysis of one-dimensional gas dynamics equations in Lagrangian coordinates and conservation laws
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2020
\vol 61
\issue 2
\pages 40--59
\mathnet{http://mi.mathnet.ru/pmtf338}
\crossref{https://doi.org/10.15372/PMTF20200205}
\elib{https://elibrary.ru/item.asp?id=42694446}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2020
\vol 61
\issue 2
\pages 189--206
\crossref{https://doi.org/10.1134/S0021894420020054}
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  • https://www.mathnet.ru/eng/pmtf/v61/i2/p40
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
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